5.8. Examination of price data for a given stock reveals that the stock has a 41% probability of increasing by 42% in any given 6-month period and a 59% probability of decreasing by 30% during any 6-month period. The stock has a current market value equal to $60; a 1-year call option exists on the stock with an exercise price equal to $50. Assume an annual riskless return rate equal to 5% and that it is compounded continuously. a. What is the probability that the stock's price will exceed $100 at the end of 6 months? b. What is the probability that the stock's price will exceed $100 at the end of 1 year? (One year represents two 6-month intervals.) c. What are the two potential stock prices at the end of the first 6-month period? What are the probabilities associated with each of these prices? d. What are the three potential stock prices at the end of the second 6-month period? What are the probabilities associated with each of these prices? e. What are the three potential call option values at the end of 1 year? That is, what would be the value of the call option conditional on each of the three potential stock prices being realized? f. If the stock price increases during the first 6-month period, two potential stock prices are possible at the end of 1 year. What are these two prices? What are the potential call values? Based on these two potential prices and associated probabilities, what would be the value of the call option if the stock price increases during the first 6-month period? Note that we are pricing the call based upon the physical probabilities, so that we will not obtain risk-neutral pricing. g. If the stock price decreases during the first 6-month period, two potential stock prices are possible at the end of 1 year. What are these two prices? What are the potential call values? Based on these two potential prices and associated probabilities, what would be the value of the call option if the stock price decreases during the first 6-month period? h. Based on the two potential call option values estimated in parts f and g and their associated probabilities, what is the current value of the call